This file NOAA's GOES-13 weather satellite image shows the storm system associated with Superstorm Sandy covering the northeastern United States before landfall.

Six months after Superstorm Sandy killed dozens of people and caused an estimated $50 billion in damage on the East Coast, a majority — 58 percent — of Americans see a connection between recent changes in the weather and global climate change, according to a new report.

"People are beginning to recognize a pattern of extreme weather across the country and are themselves saying 'Aha, I wonder if climate change has something to do with that,'" Anthony Leiserowitz, director of the Yale Project on Climate Change Communication, which released the report today, told NBC News.

Climate scientists are typically careful not to draw too close of an association between climate change and the day-to-day weather, notes Leiserowitz. The standard talking point is that no single weather event is caused by climate change. Still, climate change may be making the usual weather worse.

"The report provides good evidence for why it is we rely on science rather than public opinion on such matters," Roger Pielke Jr., from the Center for Science and Technology Policy Research at the University of Colorado, said in an email to NBC News. Pielke was not involved with the Yale survey, but has written extensively on climate change policy.

"The attribution of changes in climate on extremes is a difficult and thorny scientific puzzle requiring long-term data," he added. "Unfortunately, the human experience — in one place at a time and over a generation — is not a solid basis for such attribution."

In recent years, however, climate science has evolved to the point where some researchers are beginning to see the fingerprint of climate change on individual heat waves, droughts, hurricanes, and other storms.

These so-called attribution studies calculate the likelihood that events such as the Russian heat wave of 2010 and the drought in Texas and Oklahoma in 2011 could have occurred in the absence of climate change.

The answer is "very, very small ... so that basic line has begun to shift even among the climate science community," Leiserowitz said.

The American people, he added, "are not empty vessels waiting to be told to think about these issues by scientists or journalists, they are actively interpreting their own experience and what we are seeing in our data is that many Americans are now connecting the dots."

The connections the public is drawing between extreme weather events and climate change are consistent with the climate science, Leiserowitz said. While climate change doesn't necessarily cause the weather events, adding greenhouse gases to the Earth's weather system has an effect similar to giving steroids to a baseball player: Harder hits. It juices the system, he said.

And the picture the connected dots present shows climate change making life harder — about two out of three Americans said the weather has been "worse" over the past couple years, which is up 12 percentage points from 2012. Only 11 percent said the weather has gotten better, down 16 points.

In addition, just over half believe extreme weather will cause a natural disaster in their community in the next year.

That said, only one in three Americans are actually prepared for an extreme weather event, highlighting the need for people to develop an emergency plan and kit and get "ready for the unknown event that is going to happen in your lifetime at some point," Leiserowitz said.

The survey is based on interviews with 1,045 adults between April 8 and 15 with a margin of error of +/- 3 percentage points.

John Roach is a contributing writer for NBC News. To learn more about him, visit his website.